20150715_FloydRoseKinematics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this post, we'll have a look at the kinematics of the [Floyd Rose tremolo](https://en.wikipedia.org/wiki/Floyd_Rose).\n",
    "\n",
    "For those that have never heard about it, this is a tremolo system that allows electric guitars to produce interesting vibrato-like sounds. For instance, you can sound like a motorbike:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import YouTubeVideo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/2rUzwv7hZTI\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x4059208>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"2rUzwv7hZTI\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The way the tremolo works is simple: the strings are not fixed directly to the body of the guitar but to a spring that is fixed to the body of the guitar. A good illustration can be found on wikipedia:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/0/05/Floyd_Rose.svg/1000px-Floyd_Rose.svg.png\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(url=\"https://upload.wikimedia.org/wikipedia/commons/thumb/0/05/Floyd_Rose.svg/1000px-Floyd_Rose.svg.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the key things to understand when trying to think about this tremolo is the way it changes shape when tuning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.html.widgets import interact, fixed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyzing the rotation of a vector "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider the following case: we rotate a vector $\\vec{OM}$ defined by its length, $l$, and an angle, $\\alpha$. \n",
    "\n",
    "The coordinates of the point $M = (x, y)$ are computed as follows:\n",
    "$$x = l \\cos{\\alpha}$$\n",
    "$$y = l \\sin{\\alpha}$$\n",
    "\n",
    "We can plot this using the following interactive function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_vector(alpha, l=1):\n",
    "    x = l * np.cos(alpha)\n",
    "    y = l * np.sin(alpha)\n",
    "    ax = plt.gca()\n",
    "    ax.add_artist(plt.Circle((0, 0), l, fill='False', fc='white'))\n",
    "    ax.arrow(0, 0, x, y, head_width=0.05, head_length=0.1, fc='r', ec='k')\n",
    "    plt.xlim(-l*1.1, l*1.1)\n",
    "    plt.ylim(-l*1.1, l*1.1)\n",
    "    plt.title(\"alpha = {} rad\".format(alpha))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MmaJ2CTEnIyMDCxYssK5fv9556aWXPmO32w8T0Y2k5elEESQ99xgWWhj6nzqd7qpnn33W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\nX+6e0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcb793c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(plot_vector, \n",
    "        alpha=(0, 6.28, 0.1),\n",
    "        l=fixed(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can do an animated version of this using JSAnimation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<div class=\"animation\" align=\"center\">\n",
       "    <img id=\"_anim_imgNVRRVDORWXFNVOVI\">\n",
       "    <br>\n",
       "    <input id=\"_anim_sliderNVRRVDORWXFNVOVI\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animNVRRVDORWXFNVOVI.set_frame(parseInt(this.value));\"></input>\n",
       "    <br>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.slower()\">&#8211;</button>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.previous_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAgyTCyQ6wAAANRJREFUKM9jYBjO4AiUfgzFGGAp4+yayUvX6jMwMDCsYmBgOCS4OAOrSYmMgcc8/pd5Q3irC+Neh/1AlmeBMVgZmP8yMLD8/c/cqv9r90whzv/MX7Eq/MfAwMDIwCuZdfSV8U8WDgZGRmYGrAoZGRgY/jO8b3sj/J2F6T8j4z80pzEhmIwMjAxsSbqqlkeZGP//Z8SlkJnhPwMjwx/Guoe1NhmRwk+YGH5jV8jOwMPHzcDBysAwh8FrxQwtPU99HrwBXsnAwMDAsJiBgYGBoZ1xmKYqALHhMpn1o7igAAAAAElFTkSuQmCC\"></button>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.pause_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAkR91DQ2AAAAKtJREFUKM9jYCANTEVib2K4jcRbzQihGWEC00JuNjN8Z2Q0Zo3VYWA4lL005venH9+c3ZK5IfIsMIXMBtc12Bj+MMgxMDAwMPzWe2TBzPCf4SLcZCYY4/9/RgZGBiaYFf8gljFhKiQERhUOeoX/Gf8y/GX4y/APmlj+Mfxj+MfwH64Qnnq0zr9fyfLrPzP3eQYGBobvk5x4GX4xMIij23gdib0cRWYHiVmAAQDK5ircshCbHQAAAABJRU5ErkJggg==\"></button>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAkd/uac8wAAAMhJREFUKM9jYBie4DEUQ8B+fEq3+3UrMzAwMFxjYGBgYJizYubaOUxYFUaXh/6vWfRfEMIL/+//P5gZJoei4/f/7wxnY1PeNUXdE2RgYGZgYoCrY2BBVsjKwMDAwvCS4f3SG/dXxm5gYESSQ1HIwvCPgZmB8f8Pxv+Kxxb/YfiPJIdi9T8GJgaG/38ZFd4Fx0xUYsZt4h8GBgb2D2bLy7KnMTAwMEIxFoVCXIYr1IoDnkF4XAysqNIwUMDAwMDAsADKS2NkGL4AAIARMlfNIfZMAAAAAElFTkSuQmCC\"></button>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
       "    <button onclick=\"animNVRRVDORWXFNVOVI.faster()\">+</button>\n",
       "  <form action=\"#n\" name=\"_anim_loop_selectNVRRVDORWXFNVOVI\" class=\"anim_control\">\n",
       "    <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
       "    <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
       "    <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
       "  </form>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgNVRRVDORWXFNVOVI\";\n",
       "    var slider_id = \"_anim_sliderNVRRVDORWXFNVOVI\";\n",
       "    var loop_select_id = \"_anim_loop_selectNVRRVDORWXFNVOVI\";\n",
       "    var frames = new Array(0);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,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\"\n",
       "  frames[1] = 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\"\n",
       "  frames[2] = 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\"\n",
       "  frames[3] = 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\"\n",
       "  frames[4] = 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\"\n",
       "  frames[5] = 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Ly9XSkqKBg8erJKSEoe7BgA4wVVHYKFk0qcIAHALk/adrprEAQBAdxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACMRYAAAIxFgAAAjEWAAACNFOt3A1zU0NGju3Lk6fvy4vF6vXnnlFQ0dOrRdndfr1ZAhQzRgwABFRUWpqqrKgW4BAE5y1RFYUVGRcnNzdfjwYU2dOlVFRUUd1lmWJb/frwMHDhBeANBPuSrAtm3bpsLCQklSYWGhtm7d2mmtbdvhagsA4EKuCrD6+nrFx8dLkuLj41VfX99hnWVZuvPOOzVp0iQ9//zz4WwRAOASYT8Hlpubq7q6una3P/30022WLcuSZVkdPsfevXuVkJCgzz77TLm5uUpLS1NOTs516RcA4E5hD7CdO3d2el98fLzq6uo0atQonTp1SiNHjuywLiEhQZI0YsQI3XvvvaqqquowwJYvXx687vP55PP5etU7APQ1fr9ffr/f6TauiWW76GTS0qVLdcMNN+jJJ59UUVGRGhsb203kuHDhglpbWxUTE6OmpiZNmzZNy5Yt07Rp09rUWZbFeTIA6CGT9p2uCrCGhgbNmTNHJ06caDON/uTJk/rpT3+q7du365NPPtEPf/hDSVJLS4seeOAB/epXv2r3XCb9EADALUzad7oqwELJpB8CALiFSftOV81CBACguwgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJEIMACAkQgwAICRCDAAgJFcE2BbtmxRRkaGBgwYoP3793daV1FRobS0NKWmpmrVqlVh7BAA4CauCbCbb75Zr7/+um6//fZOa1pbW7V48WJVVFSourpapaWlOnToUBi7BAC4RaTTDXwlLS2ty5qqqiqlpKTI6/VKkgoKClRWVqb09PTr3B0AwG1ccwTWHbW1tUpKSgouezwe1dbWOtgRAMApYT0Cy83NVV1dXbvbV65cqVmzZnX5eMuyrkdbAAADhTXAdu7c2avHJyYmKhAIBJcDgYA8Hk+n9cuXLw9e9/l88vl8vXp9AOhr/H6//H6/021cE8u2bdvpJr7u+9//vlavXq1bb7213X0tLS0aN26cdu3apdGjRys7O1ulpaUdngOzLEsue2sA4Hom7Ttdcw7s9ddfV1JSkiorK3XXXXdp5syZkqSTJ0/qrrvukiRFRkaquLhY06dP1/jx4zV37lwmcABAP+W6I7BQMelTBAC4hUn7TtccgQEA0BMEGADASARYB0ydkeMU1lfPsL56hvXVc/1lnRFgHegvP/xQYX31DOurZ1hfPddf1hkBBgAwEgEGADBSn55GDwDoOVNiwTX/jT7UTPkBAACuDUOIAAAjEWAAACMRYJK2bNmijIwMDRgwQPv37++0rqKiQmlpaUpNTdWqVavC2KG7NDQ0KDc3V2PHjtW0adPU2NjYYZ3X69Utt9yirKwsZWdnh7lL53Vne1myZIlSU1OVmZmpAwcOhLlDd+lqffn9fsXGxiorK0tZWVl66qmnHOjSPR588EHFx8fr5ptv7rSmz29fNuxDhw7ZH3/8se3z+ewPP/yww5qWlhY7OTnZ/vTTT+3m5mY7MzPTrq6uDnOn7vDEE0/Yq1atsm3btouKiuwnn3yywzqv12ufPn06nK25Rne2l+3bt9szZ860bdu2Kysr7cmTJzvRqit0Z32988479qxZsxzq0H3ee+89e//+/faECRM6vL8/bF8cgUlKS0vT2LFjr1pTVVWllJQUeb1eRUVFqaCgQGVlZWHq0F22bdumwsJCSVJhYaG2bt3aaa3dTyfTdGd7+fp6nDx5shobG1VfX+9Eu47r7u9Xf92eOpKTk6O4uLhO7+8P2xcB1k21tbVKSkoKLns8HtXW1jrYkXPq6+sVHx8vSYqPj+/0l8KyLN15552aNGmSnn/++XC26LjubC8d1dTU1IStRzfpzvqyLEv79u1TZmam8vLyVF1dHe42jdIftq8+O43+Srm5uaqrq2t3+8qVKzVr1qwuH9/f/q6ss/X19NNPt1m2LKvTdbN3714lJCTos88+U25urtLS0pSTk3Nd+nWb7m4vVx5R9Lft7Cvded8TJ05UIBBQdHS0duzYofz8fB0+fDgM3Zmrr29f/SbAdu7c2avHJyYmKhAIBJcDgYA8Hk9v23Ktq62v+Ph41dXVadSoUTp16pRGjhzZYV1CQoIkacSIEbr33ntVVVXVbwKsO9vLlTU1NTVKTEwMW49u0p31FRMTE7w+c+ZMPfLII2poaNCwYcPC1qdJ+sP2xRDiFTobY580aZKOHDmiY8eOqbm5WS+//LJmz54d5u7cYfbs2dq0aZMkadOmTcrPz29Xc+HCBZ0/f16S1NTUpLfeeuuqs6X6mu5sL7Nnz9bmzZslSZWVlRo6dGhwaLa/6c76qq+vD/5+VlVVybZtwusq+sX25eAEEtf4y1/+Yns8HnvgwIF2fHy8PWPGDNu2bbu2ttbOy8sL1pWXl9tjx461k5OT7ZUrVzrVruNOnz5tT5061U5NTbVzc3PtM2fO2Lbddn3961//sjMzM+3MzEw7IyOjX66vjraXdevW2evWrQvWPProo3ZycrJ9yy23dDoDtr/oan0VFxfbGRkZdmZmpn3bbbfZ77//vpPtOq6goMBOSEiwo6KibI/HY7/wwgv9bvvqs/8LEQDQtzGECAAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADDS/wGPrrGvO9J9sAAAAABJRU5ErkJggg==\"\n",
       "  frames[6] = 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BBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEj/B8VO/t7nV9itAAAAAElFTkSuQmCC\"\n",
       "  frames[7] = 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\"\n",
       "  frames[8] = 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       "  frames[9] = 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\"\n",
       "  frames[10] = 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       "  frames[11] = 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f/21CgoK5PV6A043JkmzZ8/WzJkzlZqayq5AoIMiwOB69fX1Kikpkdfr1VtvvRXQPmbMGM2ePVtjxozRJZdcEoQKAQQDAQZXMcbo448/1ooVK/Tss88GtF9++eXyeDzKy8tT7969g1AhALcgwBBUdXV1Wrt2rbxer3bu3BnQ/tBDD+mRRx7RiBEj2BUIoBkCDO2moaFBb775ppYuXari4uKA9muvvVYej0c333wzJ7oFcFYEGC4KY4x27NihlStXasmSJTp16lSz9tjYWHk8Ht13333q27dvkKoEYDMCDBfEkSNHtG7dOnm9XlVWVga033333Xr00UeVkZGhkBBX/QwdAEsRYDhnTU1Nevfdd+X1erV+/fqA9szMTHk8Hk2ePJkzsQO4aAgwnNWuXbv8Z2I/ceJEs7YePXr4z8SemJgYpAoBdEYEGJo5fvy4Xn31VS1ZskQVFRUB7bfddptmzZql0aNHcyZ2AEFFgHVip06dUllZmZYuXaqXX345oP2qq66Sx+PRrbfequ7duwehQgBoHQHWiVRXV+vPf/6zvF6vamtrm7V17drVfyb2/v37B6lCAGg7AqyD+vbbb7VhwwZ5vV6VlZUFtE+aNEmzZ8/Wddddx5nYAViJLVcHcOrUKW3btk3Lly/XmjVrAtpTU1Pl8Xh0++23Kyoqqv0LBICLgACzUE1NjQoKCrRkyRIdOHCgWZvjOPJ4PHr44Yc1aNAgTr8EoMMiwFzu5MmTKi4ultfrlc/nC2gfN26cZs+erZycHHXp0qX9CwSAICHAXMQYo+3bt2vFihVauXJlQPuVV14pj8eju+66S7169QpChQDgHgRYEB08eNB/Jvbdu3cHtD/88MOaOXOmhg8fzq5AADgNAdZOGhoatGnTJi1dulSlpaUB7ddff71mz56t3NxczsQOAG1AgLXR0aNHtXXrVo0dO/asfY0x+uyzz/Tss8/K6/UGtMfFxcnj8ejee+9VbGzsxSgXADo8AuwsPv74Yz37P/+jl156SfVNTarYvl0pKSnN+hw+fFgvvfSSvF6vPv3004DnuOeeezRr1iyNHDmSXYEAcIE4xhgT7CIuBsdxdL6L1tDQoA0bNmjFokX6rLJSD9bX68GmJq0ODdWuqVN110MPyev1qqioKOCxo0ePlsfj0aRJk3TZZZf92MUAgHb1Y7ad7Y0A+4Hq6mqtWr5cz69YoZSmJj167JgmS7rk/9v/I+mHO/yio6M1Z84cPfDAA4qPj79AlQNA8NgUYJ1+F6IxRm+//bZW/PGPeuuf/9QvjdEbJ09qWAt9YyT9KixM9XfdpeUvvNDepQIAfqDTzsAOHz6stWvWaMXixQo9dEgzjx3TFEkhko5JOt7Kv7sl/W9oqHbu3at+/fpd7MUAgHZl0wysUwZYfX29+vTqpSPHjkmSwsPC9F1Tk7qGhal7167q1rWrul92mbqFh6t79+7q1r27ukdGqltkpLr36KFuUVGaOHmyMjIy2nORAOCiI8Bc4GxvQmVlpS699NLvA6pbN4WHhyskJKQdKwQA9yHAXMCmNwEA3MKmbSdTDgCAlQgwAICVCDAAgJUIMACAlQgwAICVCDAAgJUIMACAlQgwAICVCDAAgJVcdTb62tpa3XbbbdqzZ4+SkpL0t7/9TT169Ajol5SUpMjISIWGhqpLly4qLy8PQrUAgGBy1QwsPz9fOTk5+vzzz3XDDTcoPz+/xX6O48jn86miooLwAoBOylUBVlRUpLy8PElSXl6eNmzY0GpfW87VBQC4OFwVYDU1NYqN/f43j2NjY1VTU9NiP8dxdOONNyojI0PPP/98e5YIAHCJdv8OLCcnRwcOHAi4/+mnn25223EcOY7T4nNs2bJFcXFx+vrrr5WTk6PU1FRlZWVdlHoBAO7U7gG2adOmVttiY2N14MAB9e3bV1999ZViYmJa7BcXFydJ6tOnj2655RaVl5e3GGDz58/3X8/OzlZ2dvaPqh0AOhqfzyefzxfsMs6Lq34PbO7cuerVq5eeeOIJ5efn69ChQwEHcpw4cUJNTU2KiIjQ8ePHNWbMGM2bN09jxoxp1s+m37QBALewadvpqgCrra3VtGnTtHfv3maH0e/fv18PPvigNm7cqJ07d2rKlCmSpMbGRt1xxx168sknA57LpjcBANzCpm2nqwLsQrLpTQAAt7Bp2+mqoxABAGgrAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJQIMAGAlAgwAYCUCDABgJdcE2CuvvKKhQ4cqNDRU27Zta7VfaWmpUlNTlZKSokWLFrVjhQAAN3FNgA0fPlzr16/Xtdde22qfpqYmzZo1S6WlpaqsrNS6dev0ySeftGOVAAC3CAt2Af+Vmpp61j7l5eVKTk5WUlKSJGn69OkqLCzU4MGDL3J1AAC3cc0MrC2qq6uVmJjov52QkKDq6uogVgQACJZ2nYHl5OTowIEDAfcvXLhQEyZMOOvjHce5GGUBACzUrgG2adOmH/X4+Ph4VVVV+W9XVVUpISGh1f7z58/3X8/OzlZ2dvaPen0A6Gh8Pp98Pl+wyzgvjjHGBLuIH7r++uu1ePFiXX311QFtjY2NGjRokN58803169dPo0aN0rp161r8DsxxHLls0QDA9WzadrrmO7D169crMTFRZWVluummmzR+/HhJ0v79+3XTTTdJksLCwrRs2TKNHTtWQ4YM0W233cYBHADQSbluBnah2PS/CABwC5u2na6ZgQEAcC4IMACAlQiwFth6RE6wMF7nhvE6N4zXuessY0aAtaCzvPkXCuN1bhivc8N4nbvOMmYEGADASgQYAMBKHfowegDAubMlFlxzNvoLzZY3AABwftiFCACwEgEGALASASbplVde0dChQxUaGqpt27a12q+0tFSpqalKSUnRokWL2rFCd6mtrVVOTo4GDhyoMWPG6NChQy32S0pK0ogRI5Senq5Ro0a1c5XB15b1xePxKCUlRWlpaaqoqGjnCt3lbOPl8/kUFRWl9PR0paena8GCBUGo0j3uu+8+xcbGavjw4a326fDrl4H55JNPzGeffWays7PNhx9+2GKfxsZGM2DAALNr1y5TX19v0tLSTGVlZTtX6g6PP/64WbRokTHGmPz8fPPEE0+02C8pKckcPHiwPUtzjbasLxs3bjTjx483xhhTVlZmMjMzg1GqK7RlvN5++20zYcKEIFXoPu+8847Ztm2bGTZsWIvtnWH9YgYmKTU1VQMHDjxjn/LyciUnJyspKUldunTR9OnTVVhY2E4VuktRUZHy8vIkSXl5edqwYUOrfU0nPZimLevLD8cxMzNThw4dUk1NTTDKDbq2fr466/rUkqysLEVHR7fa3hnWLwKsjaqrq5WYmOi/nZCQoOrq6iBWFDw1NTWKjY2VJMXGxrb6oXAcRzfeeKMyMjL0/PPPt2eJQdeW9aWlPvv27Wu3Gt2kLePlOI62bt2qtLQ05ebmqrKysr3LtEpnWL867GH0p8vJydGBAwcC7l+4cKEmTJhw1sd3tr8ra228nn766Wa3HcdpdWy2bNmiuLg4ff3118rJyVFqaqqysrIuSr1u09b15fQZRWdbz/6rLcs9cuRIVVVVKTw8XCUlJZo8ebI+//zzdqjOXh19/eo0AbZp06Yf9fj4+HhVVVX5b1dVVSkhIeHHluVaZxqv2NhYHThwQH379tVXX32lmJiYFvvFxcVJkvr06aNbbrlF5eXlnSbA2rK+nN5n3759io+Pb7ca3aQt4xUREeG/Pn78eD3yyCOqra1Vz549261Om3SG9YtdiKdpbR97RkaGduzYod27d6u+vl5//etfNXHixHauzh0mTpyoF198UZL04osvavLkyQF9Tpw4oaNHj0qSjh8/rjfeeOOMR0t1NG1ZXyZOnKi1a9dKksrKytSjRw//rtnOpi3jVVNT4/98lpeXyxhDeJ1Bp1i/gngAiWv8/e9/NwkJCaZr164mNjbWjBs3zhhjTHV1tcnNzfX3Ky4uNgMHDjQDBgwwCxcuDFa5QXfw4EFzww03mJSUFJOTk2Pq6uqMMc3H68svvzRpaWkmLS3NDB06tFOOV0vry8qVK83KlSv9fR599FEzYMAAM2LEiFaPgO0szjZey5YtM0OHDjVpaWlm9OjR5r333gtmuUE3ffp0ExcXZ7p06WISEhLM6tWrO9361WHPhQgA6NjYhQgAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCw0v8Bzdd2ZV8IwpwAAAAASUVORK5CYII=\"\n",
       "  frames[12] = 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RllZme6ZPFnznnxSktQ/OVmrMzLUuHFjlysDcC4IMNR6JSUlGnvHHXrxpZckSSNHjNCyl19WgwYNXK4MwE9BgKHWOnLkiEZdf70y33xTknTn2LF6ev58hYSEuFwZgPOBa2Codb799lv16tlToaGhynzzTf3PvfeqtLRUzz3/POEF1CIcgaHWOHDggK7q00c7d+2SJM2aNUv3338/N9gFaikCDNbLyclRYmKiCgsLJUlPPvmkJkyYQHABtRwBBmvt3LlTnTp1Cky/+OKLuuWWW1ysCEBNIsBgnU8//VSXX355YPqNN97Qdddd52JFANxAgMEamzZtUr9+/QLTPp9PV199tYsVAXATAQbPy8zM1NChQwPTH330ka644goXKwLgBQyjh2ctX75cjuMEwmv79u0yxhBeACQRYPAYY4yeffZZOY6j9PR0hYWFac+ePTLGKD4+3u3yAHgIAQZPMMbokUceUVBQkMaNG6dLLr5Y+fn5+vbbb3XJJZe4XR4ADyLA4KoTJ07o/91/v4KCgjR16lR1T0pSUVGR9uzdq/DwcLfLA+BhDOKAK0pLSzXx7rv1zIIFkqSBAwZo5apVatSokcuVAbAFAYYadezYMf3yF7/Q8ldflSTd+POfa+nf/qaLLrrI5coA2IYAQ404fPiwRgwfrnXvvCNJGj9unOY9+aSCg9kEAZwbroHhgiouLlb3pCQ1btxY6955R7+bNk1lZWWa/8wzhBeAn4Q9CC6IgoIC9erZU3v37ZMkzZ07V/fddx832AVw3hBgOK/27dunrl276tChQ5KkBQsW6Fe/+hXBBeC8I8BwXnzxxRfq3LlzYPqVV15Renq6ixUBqO0IMPwkW7duLXdrpzVr1mjIkCEuVgSgriDAcE42bNhQ7k7w7733nvr27etiRQDqGgIMZ2X16tXlvnvrX//6lxITE12sCEBdxTB6VMtLL70kx3EC4bVjxw4ZYwgvAK4hwFAlY4yeeuopOY6jW2+9VS1btpTf75cxRnFxcW6XB6COI8BQgTFGs2fPVlBQkO6++27Fxcbqq6++0oEDBxQVFeV2eQAgiQDDScrKynTf//yPgoKC9MADD6jnlVequLhYO3buVOvWrd0uDwDKYRAHdPz4cf1m/Hi9sHChJGnokCF69bXXFBoa6nJlAFA1AqwOO3r0qG4ePVqvr1wpSbr1llv0wsKFql+/vsuVAcCZEWB10Hfffadr09K0YeNGSdLEu+/Wn//yF26uC8AqntpjFRYW6qabbtLevXsVExOjv//972rWrFmFdjExMWrSpInq1aunkJAQZWVluVCtfQoLC3V1//7a9vnnkqTp06dr5syZCgriUigA+3hqzzVnzhylpqZqx44dGjhwoObMmVNpO8dx5PP59MknnxBe1bB//35Ftmunli1batvnn+uxxx7TiRMn9NBDDxFeAKzlGGOM20X8KD4+XuvXr1d4eLjy8/OVkpKiL774okK79u3b66OPPlLLli2rfC3HceShVXPFl19+qS5duujo0aOSpBdeeEF33HGHy1UB8DKb9p2e+ve7oKBA4eHhkqTw8HAVFBRU2s5xHA0aNEg9evTQs88+W5MlWuHzzz+X4zjq0KGDjh49qtdee03GGMILQK1S49fAUlNTlZ+fX+Hns2bNKjftOE6V3yG1adMmRURE6Ouvv1Zqaqri4+OVnJx8Qeq1yYcffqiePXsGpteuXatBgwa5WBEAXDg1HmBr166tct6Ppw7btm2r/fv3q02bNpW2i4iIkCS1bt1a119/vbKysioNsJkzZwaep6SkKCUl5SfV7lXvvPOOBg4cGJjevHmzevfu7WJFAGzh8/nk8/ncLuOceOoa2NSpU9WyZUtNmzZNc+bMUXFxcYWBHN9//73KysoUFhamw4cPa/DgwZoxY4YGDx5crp1N53HP1cqVKzVy5MjA9GeffaZu3bq5WBEA29m07/RUgBUWFio9PV379u0rN4w+Ly9Pv/71r7V69Wrt3r1bo0aNkiSVlpbq1ltv1f3331/htWz6JZytJUuWaMyYMZKk+vXrKzs7Wx07dnS5KgC1gU37Tk8F2Plk0y+hOowxeuKJJzR58mRJUtvwcH28davatWvncmUAahOb9p2eGoWIik6cOKEHH3xQQUFBmjx5srp07qwDBw5of34+4QWgTvPUnTjwf8rKynTvlCn66+OPS5L69e2rjDVrFBYW5nJlAOANHIG5pKysTNN/9zut+uFGuj86fvy4bvvlLxUcHKy/Pv64hg8bpiNHjmjje+8RXgBwEq6BuaCwsFC3jBih7z7+WLskzZ03T+k336wbf/5zrc7IkCTdfvvtWrBggUJCQtwtFkCd4uV956kIsBr26aefatSQIRpRWKg/lpRol6TOJ83/7T336JFHH1W9evXcKhFAHebVfWdlOIVYg5a9+KIGXXWVfp+fr8dKShQsKV7Sph/m/27KFP3psccILwCoBo7AakBpaammTp6slYsW6R/ff6/EStr8W1L/evV046236ukXXiDEALjCS/vOM2EU4gX21Vdf6abrrtNF27bpwyNH1OKHnx+StEHS2vr19fZFFymvrEwD+/VT9969dejQoUq/Bw0A8H84AruAPvzwQ/08LU2/LC7W9NJSbZW0NihIbzdurE+OHtWVXbsqddQoDRo8WN27d+eoC4DrvLDvrC4C7AJ54dlnddeECer7w30bfceOKSYyUqnDhmlQWpqSk5MVGhrqWn0AUBm3951ngwC7AJa//LLSb75Z0S1aKHXwYA0aPlwDBw6s8u76AOAVBJgHuPlLOHTokPbv36+4uLgqv9MMALyIAPMAm34JAOAVNu07+RwYAMBKBBgAwEoEGADASgQYAMBKBBgAwEoEGADASgQYAMBKBBgAwEoEGADASgQYAMBKBBgAwEoEGADASgQYAMBKBBgAwEoEGADASgQYAMBKBBgAwEoEGADASgQYAMBKBBgAwEoEGADASgQYAMBKBBgAwEoEGADASgQYAMBKBBgAwEoEGADASgQYAMBKBBgAwEqeCbDly5crISFB9erV09atW6tsl5mZqfj4eMXFxWnu3Lk1WCEAwEs8E2DdunXTihUr1L9//yrblJWVaeLEicrMzFR2draWLVum7du312CVAACvCHa7gB/Fx8efsU1WVpZiY2MVExMjSRo9erRWrlypzp07X+DqAABe45kjsOrIzc1VdHR0YDoqKkq5ubkuVgQAcEuNHoGlpqYqPz+/ws9nz56tYcOGnXF5x3EuRFkAAAvVaICtXbv2Jy0fGRkpv98fmPb7/YqKiqqy/cyZMwPPU1JSlJKS8pPeHwBqG5/PJ5/P53YZ58Qxxhi3izjZz372Mz366KO64oorKswrLS3VpZdeqnXr1qldu3bq2bOnli1bVuk1MMdx5LFVAwDPs2nf6ZlrYCtWrFB0dLS2bNmia6+9VkOHDpUk5eXl6dprr5UkBQcHa968ebrmmmvUpUsX3XTTTQzgAIA6ynNHYOeLTf9FAIBX2LTv9MwRGAAAZ4MAAwBYiQCrhK0jctxCf50d+uvs0F9nr670GQFWibryyz9f6K+zQ3+dHfrr7NWVPiPAAABWIsAAAFaq1cPoAQBnz5ZY8Mzd6M83W34BAIBzwylEAICVCDAAgJUIMEnLly9XQkKC6tWrp61bt1bZLjMzU/Hx8YqLi9PcuXNrsEJvKSwsVGpqqjp16qTBgweruLi40nYxMTG67LLLlJSUpJ49e9Zwle6rzvYyadIkxcXFKTExUZ988kkNV+gtZ+ovn8+npk2bKikpSUlJSXr44YddqNI7xo4dq/DwcHXr1q3KNrV++zIw27dvN//5z39MSkqK+fjjjyttU1paajp27Gi+/PJLU1JSYhITE012dnYNV+oN9913n5k7d64xxpg5c+aYadOmVdouJibGHDx4sCZL84zqbC+rV682Q4cONcYYs2XLFtOrVy83SvWE6vTXu+++a4YNG+ZShd6zYcMGs3XrVtO1a9dK59eF7YsjMEnx8fHq1KnTadtkZWUpNjZWMTExCgkJ0ejRo7Vy5coaqtBbVq1apTFjxkiSxowZo9dff73KtqaODqapzvZycj/26tVLxcXFKigocKNc11X376uubk+VSU5OVvPmzaucXxe2LwKsmnJzcxUdHR2YjoqKUm5urosVuaegoEDh4eGSpPDw8Cr/KBzH0aBBg9SjRw89++yzNVmi66qzvVTWJicnp8Zq9JLq9JfjOHr//feVmJiotLQ0ZWdn13SZVqkL21etHUZ/qtTUVOXn51f4+ezZszVs2LAzLl/XPldWVX/NmjWr3LTjOFX2zaZNmxQREaGvv/5aqampio+PV3Jy8gWp12uqu72cekRR17azH1Vnvbt37y6/36/Q0FCtWbNGI0eO1I4dO2qgOnvV9u2rzgTY2rVrf9LykZGR8vv9gWm/36+oqKifWpZnna6/wsPDlZ+fr7Zt22r//v1q06ZNpe0iIiIkSa1bt9b111+vrKysOhNg1dleTm2Tk5OjyMjIGqvRS6rTX2FhYYHnQ4cO1V133aXCwkK1aNGixuq0SV3YvjiFeIqqzrH36NFDO3fu1J49e1RSUqJXXnlFw4cPr+HqvGH48OFavHixJGnx4sUaOXJkhTbff/+9Dh06JEk6fPiw3nrrrdOOlqptqrO9DB8+XEuWLJEkbdmyRc2aNQucmq1rqtNfBQUFgb/PrKwsGWMIr9OoE9uXiwNIPOMf//iHiYqKMg0aNDDh4eFmyJAhxhhjcnNzTVpaWqBdRkaG6dSpk+nYsaOZPXu2W+W67uDBg2bgwIEmLi7OpKammqKiImNM+f7673//axITE01iYqJJSEiok/1V2fYyf/58M3/+/ECbu+++23Ts2NFcdtllVY6ArSvO1F/z5s0zCQkJJjEx0fTp08ds3rzZzXJdN3r0aBMREWFCQkJMVFSUef755+vc9lVr74UIAKjdOIUIALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsBIBBgCwEgEGALASAQYAsNL/Bxg7V6x5c66vAAAAAElFTkSuQmCC\"\n",
       "  frames[13] = 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derUSS6XS2vXrlVaWprdkQCvQoEB1+HixYu64YYbJEk7d+7UHXfcYXMiwPtQYMA1OnXqlIKCgiRJR44c0a233mpzIsA7UWDANSgrK3N/QkJFRYWCg4NtTgR4L6bRAy20Z88ed3mdP3+e8gJsRoEBLbB+/Xr169dP0qWP/fn89S8A9qHAgKvIzc3ViBEj1Ou22+RyueTr62t3JACiwIAr+vmiRXr44YeVPmaM/nXoEGfXADwIBQY0Y8Z3v6s5P/iBnpw1S6vXrLE7DoDLMAsRaMKoESNUtH69/uuXv9RTTz9tdxwATaDAgC+wLEsRPXvq2PHjWrFihb7+9a/bHQlAMygw4N/q6urcn921YcMGDRs2zOZEAK6EAgMknTt3Tp07d5Yk7du3TwkJCTYnAnA1FBi83meffaaQkBBJ0tGjRxUeHm5zIgAtwSxEeLVDhw65y6u6upryAgxCgcFr/f3vf1dMTIykS2eXDwwMtDkRgGtBgcErFRQU6M4771RAQID7c70AmIUCg9d54403dP/992vQgAE6c+aMfHz4MwBMxF8uvMrzP/qRHnvsMT2ckaFt27dzaijAYBQYvMbDGRl6ccEC/fj55/VWbq7dcQB8SUyjR4dnWZYGJidr565d+u1vf6tp06bZHQlAK6DA0KG5XC517txZFy5cUEFBgcaOHWt3JACthAJDh1VTU6OvfOUrki5NmR84cKDNiQC0JgoMHVJ1dbW6du0q6dKblW+77TabEwFobRQYOpxjx46pZ8+eki6dJurmm2+2ORGAtsAsRHQo+/btc5fXuXPnKC+gA6PA0GFs2LBBffv2lSTV1tbqxhtvtDkRgLZEgaFDWLFihe6++25FRkTI5XLJz4+j40BHR4HBeP/1y19q0qRJGjVihEpKSzm7BuAlKDAYbdYTT+j7zzyjmTNmaF1Rkd1xALQjjrPAWGNHj1bh2rX6+aJFenb2bLvjAGhnFBiMY1mWet12m458/LHefvttTZ482e5IAGxAgcEodXV18vf3lyQ5nU7dc889NicCYBcKDMY4f/68AgICJEl79uxRYmKizYkA2IkCgxEqKircb0ouKytzv1kZgPfyqAKrqKjQ5MmT9fHHHys6OlrvvPOOgoKCGo2Ljo5Wly5d5OvrK39/fxUXF9uQFu3l8/VBkk6dOqUuXbrYGwiAR/CoafQLFy5UWlqa9u/fr5EjR2rhwoVNjnM4HHI6ndq5cyfl1cHt3LnTXV4XLlygvAC4eVSB5efnKzMzU5KUmZmpVatWNTvWsqz2igWbvPfeexowYIB8fX1VV1fn/mgUAJA8rMDKy8sVFhYmSQoLC1N5eXmT4xwOh0aNGqVBgwbpjTfeaM+IaCc5OTkaM2aM+t1+u2pra+Xr62t3JAAept1fA0tLS9Px48cb3f7iiy82uO5wOJo9JdCmTZsUHh6uEydOKC0tTQkJCRo+fHib5EX7m5eVpax58/SNr31N77z7rt1xAHiodi+wdevWNXtfWFiYjh8/rh49eujYsWMKDQ1tclx4eLgkKSQkRA888ICKi4ubLLCsrCz35dTUVKWmpn6p7Gh7md/8ppb993/rB3Pm6GfNvAYKoPU4nU45nU67Y1wXh+VBLybNnj1bN998s+bMmaOFCxeqqqqq0USOc+fOqb6+XoGBgTp79qzuu+8+zZ07V/fdd1+DcQ6Hg9fJDGJZloYOHqyt27bpN6++qu/OmGF3JMArmbTt9KgCq6io0KRJk/TJJ580mEZ/9OhRfec739Hq1at16NAhPfjgg5IunZVhypQp+uEPf9joe5n0S/B2LpdLwcHBqq6uVn5+vsaNG2d3JMBrmbTt9KgCa00m/RK8WW1trTp16iRJ2rp1q1JSUmxOBHg3k7adHvVGZniXM2fOKDAwUJJ08OBBxcTE2JwIgEkoMNiivLxcPXr0kCR9+umnCgkJsTkRANN41PvA4B3279/vLq8zZ85QXgCuCwWGdrV582bFx8dLkmpqatS5c2ebEwEwFQWGdrNy5UrdddddCuneXS6Xy/25XgBwPSgwtItXFi/Wgw8+qLuHDdOnJ040e5YVAGgpCgxt7vtPP61ZTz6p/5w2TX/bsMHuOAA6CGYhok1NGDdO+f/zP1rw4ov64XPP2R0HQAdCgaFNWJalhPh47T9wQMuXL9cjjzxidyQAHQwFhlZXX18vP79Lq1ZRUZFGjBhhcyIAHREFhlZ14cIF3XjjjZKk3bt3q1+/fjYnAtBRUWBoNVVVVQoODpYkffLJJ4qKirI5EYCOjFmIaBUlJSXu8qqsrKS8ALQ5Cgxf2u7du3XLLbdIks6fP6+goCCbEwHwBhQYvpSioiIlJSVJuvT5bDfccIPNiQB4CwoM12358uUaNWqUEuLj5XK55Ovra3ckAF6EAsN1efGFFzR16lRNGDdO+/73fzk1FIB2R4Hhmv3no4/q+R//WM98//talZ9vdxwAXopp9Lgmdw8bpg2bNumVxYv1+BNP2B0HgBejwNAiLpdLoSEhOllRoZUrV2rixIl2RwLg5SgwXFVtba06deok6dIHUg4dOtTmRABAgeEqzp49q5tuukmS9NFHH6l37942JwKASygwNOvEiRMKDQ2VJB0/flxhYWE2JwKA/8MsRDTp4MGD7vI6ffo05QXA41BgaGTr1q2Ki4uTJNXU1LgPIQKAJ6HAvJhlWXrqiSe0bt06WZYlScrPz9eQIUMUFBSk+vp6+fv725wSAJrmsD7fcnUwDodDHfSptZq3li/XT6dPl4+Pj7rcequShw/Xa6+/rqGDB2vTBx9wdg3AC5m07aTAvFRVVZX6Rkdr5alTulPSCkkZ/77v3RUr9MCDD8rHhx10wNuYtO1kC+Wlfvzssxp34YIG69JKMFmSS1K+pPmZmeoXE6M///nPtmYEgCthGr0X2r59u1a89ZY+vHixwe0XJe318VGZy6WH09J4wzIAj0aBeRmXy6WZU6dqwfnzuvnz2yS9Lem5gAANGDZMm195hTcsA/B4FJiX+e2SJfL7+GN969/X35f0/zp3lhUVpWWvv667777bxnQA0HJM4vAiJ06cUGKvXvrLmTO6QdKcgADtCAjQz371K2U89BCTNgAYte1ki+VF5syapTEXL+q3nTrpPwICNPRHP9JHJSV6eMoUyguAcTiE6CU2btyonLff1o1+fpqWmal9CxYoJCTE7lgAcN04hOgF6urqNOCOO9QrPFyLsrMVHx9vdyQAHsqkbScF5gXef/99uVwupaam2h0FgIczadtJgQEA3EzadvLKPQDASBQYAMBIFBgAwEgUGADASB5TYCtWrFBiYqJ8fX21Y8eOZscVFhYqISFBcXFxWrRoUTsmBAB4Eo8psH79+mnlypVXPBdffX29Hn/8cRUWFmrv3r3Kzc3Vvn372jElAMBTeMyZOBISEq46pri4WLGxsYqOjpYkZWRkKC8vT3369GnjdAAAT+Mxe2AtUVZWpqioKPf1yMhIlZWV2ZgIAGCXdt0DS0tL0/HjxxvdvmDBAo0bN+6qj3c4HG0RCwBgoHYtsHXr1n2px0dERKikpMR9vaSkRJGRkc2Oz8rKcl9OTU3lVEoAcBmn0ymn02l3jOvicaeSuvfee/XSSy9p4MCBje6rq6tTfHy8ioqK1LNnT6WkpCg3N7fJ18BMOh0KAHgKk7adHvMa2MqVKxUVFaUtW7bo/vvv19ixYyVJR48e1f333y9J8vPzU3Z2tkaPHq2+fftq8uTJTOAAAC/lcXtgrcWk/yIAwFOYtO30mD0wAACuBQUGADASBdYEU2fk2IXldW1YXteG5XXtvGWZUWBN8JZffmtheV0blte1YXldO29ZZhQYAMBIFBgAwEgdeho9AODamVILHnM2+tZmyi8AAHB9OIQIADASBQYAMBIFJmnFihVKTEyUr6+vduzY0ey4wsJCJSQkKC4uTosWLWrHhJ6loqJCaWlp6t27t+677z5VVVU1OS46Olr9+/dXcnKyUlJS2jml/VqyvsyaNUtxcXFKSkrSzp072zmhZ7na8nI6neratauSk5OVnJysF154wYaUnuPRRx9VWFiY+vXr1+yYDr9+WbD27dtnffTRR1Zqaqq1ffv2JsfU1dVZMTEx1uHDh62amhorKSnJ2rt3bzsn9QzPPvustWjRIsuyLGvhwoXWnDlzmhwXHR1tnTx5sj2jeYyWrC+rV6+2xo4da1mWZW3ZssUaPHiwHVE9QkuW1/r1661x48bZlNDzvP/++9aOHTus22+/vcn7vWH9Yg9MUkJCgnr37n3FMcXFxYqNjVV0dLT8/f2VkZGhvLy8dkroWfLz85WZmSlJyszM1KpVq5oda3npZJqWrC9fXI6DBw9WVVWVysvL7Yhru5b+fXnr+tSU4cOHKzg4uNn7vWH9osBaqKysTFFRUe7rkZGRKisrszGRfcrLyxUWFiZJCgsLa/aPwuFwaNSoURo0aJDeeOON9oxou5asL02NKS0tbbeMnqQly8vhcGjz5s1KSkpSenq69u7d294xjeIN61eHnUZ/ubS0NB0/frzR7QsWLNC4ceOu+nhve19Zc8vrxRdfbHDd4XA0u2w2bdqk8PBwnThxQmlpaUpISNDw4cPbJK+naen6cvkehbetZ59ryfMeMGCASkpKFBAQoDVr1mjixInav39/O6QzV0dfv7ymwNatW/elHh8REaGSkhL39ZKSEkVGRn7ZWB7rSssrLCxMx48fV48ePXTs2DGFhoY2OS48PFySFBISogceeEDFxcVeU2AtWV8uH1NaWqqIiIh2y+hJWrK8AgMD3ZfHjh2rmTNnqqKiQt26dWu3nCbxhvWLQ4iXae4Y+6BBg3TgwAEdOXJENTU1+sMf/qDx48e3czrPMH78eC1dulSStHTpUk2cOLHRmHPnzun06dOSpLNnz2rt2rVXnC3V0bRkfRk/fryWLVsmSdqyZYuCgoLch2a9TUuWV3l5ufvvs7i4WJZlUV5X4BXrl40TSDzGn/70JysyMtK64YYb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       "  frames[14] = 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\"\n",
       "  frames[15] = 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\"\n",
       "  frames[16] = 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       "  frames[17] = 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SYAr8EZmwBCvvvqq7r77biUlJurLLVtYPxHNwqSxkwADDLJy5UoNHTpUklRbW6tWrVo5XBECjUljJwEGGOazzz7TVVddJYn1E3HpmTR2EmCAgU5fP/HQoUMKCwtzuCIECpPGTmYhAgY6ff3E9u3bq7Ky0uGKgJZHgAGGioqK0tGjRyVJXbp00bZt2xyuCGhZBBhgsNDQUP/6iUlJSfrkk08crghoOQQYYLjv108MDQ3VNddco2LeJ4YgQYABAcDj8ejIkSNK6d9fI0aM0MKFC50uCWh2BBgQICzL0qeff67bx4zRvffeq2dnzXK6JKBZEWBAgHlj2TI9+sgjeuI3v9GDP/+50+UAzYa1EIEA9Mc//Uler1ePTp2qsu3bVfzWW06XBFxyvJEZCGCvvfaasrOz1TMhQVu3bWP9RJyXSWMnAQYEuFWrVunHP/6xJNZPxPmZNHYSYEAQYP1ENJVJYycBBgSJnTt3Kj4+XhLrJ6JxJo2dzEIEgkT37t317bffSmL9RAQGAgwIIh07dqy3fuLWrVsdrgi4eAQYEGROXz+xV69eWrduncMVAReHAAOC0PfrJ7Zt21ZpaWkqKipyuiTgghFgQJDyeDw6fPiwUlNSlJWVpQULFjhdEnBBCDAgiFmWpQ2ffqo7b79d9913n56ZOdPpkoAmI8AA6PU33tDURx/V///tb/XziROdLgdoEtZCBCBJmvPHPyouLk4PP/KItn/1ld565x2nSwLOiTcyA6hnyZIluuuuu5TQo4e2ffUV6ycGGZPGTgIMwFl8Pp9uvPFGSayfGGxMGjsJMAAN+vzzz5WSkiJJOn78uC6//HKHK0JLMGnsJMAANGrXrl3q3r27JOngwYNq3769wxWhuZk0djILEUCjunXr5l8/MTw8XPv27XO4IuD/EGAAzun09RNjYmJYPxGuQYABOK8z108sKSlxuCKAAAPQRN+vnxgWFqb09HQVFhY6XRKCnKsCrKqqSpmZmerVq5eGDRum6urqBtvFx8drwIABSk1NVVpaWgtXCQQvj8ejgwcPauBVV2nkyJHKy8tzuiQEMVcFWG5urjIzM7VlyxYNHTpUubm5DbazLEs+n08bN27kUgbQwizL0vqNGzX2jjt0//33a+bvfud0SQhSrgqwFStWKCcnR5KUk5Oj5cuXN9rWlGmeQKBasnSpfjV1qn775JN6YMIEp8tBEHLV+8AiIiJ04MABSf8NqMjISP/26RISEhQeHq5WrVpp4sSJmtDAL49J72UATDb3L3/RQw8/rKE33qh3Vq50uhz8QCaNnS2+mG9mZmaD7yV55pln6m1bltXoGmwffPCBYmJi9M033ygzM1PJyckaMmRIs9QL4NymPPSQYrp21bhx49QjPl7by8pYPxEtosUD7O233250X3R0tPbt26cuXbpo79696ty5c4PtYmJiJEmdOnXSbbfdppKSkgYDbMaMGf7bGRkZysjI+EG1A2jY2LFj5fP5lJGRIY/Hw/qJBvH5fPL5fE6XcVFcdQlx2rRp6tixox5//HHl5uaqurr6rIkcx44d80/lPXr0qIYNG6bp06dr2LBh9dqZdBoMBIpNmzZpwIABklg/0VQmjZ2uCrCqqiqNGzdOu3btUnx8vJYsWaIOHTpoz549mjBhggoKCrR9+3bdfvvtkv67SvZPfvIT/frXvz7rsUz6IQCBhPUTzWbS2OmqALuUTPohAIGmqqpKHTt2lCTt3btXXbp0cbgiNJVJY6erptEDCAyRkZH11k/csmWLwxUhEBFgAJpFaGioTp48KUnq3bu3Pv74Y4crQqAhwAA0m5CQENXV1al9+/YaPHiwCgoKnC4JAYQAA9CsPB6PqqurNWjgQN1yyy165ZVXnC4JAYIAA9DsLMvSuvXrddfYsRo/frx+9/TTTpeEAECAAWgxry5ZommPPaYnp0/XhPHjnS4HhmMaPYAW9/zcuZry0EP6cUaG3l21yulycBqTxk4CDIAjli5dqrFjx6pbXJx27NzJ+okuYdLYSYABcMx7773nX6OU9RPdwaSxkwAD4KjNmzerf//+klg/0Q1MGjsJMACOY/1E9zBp7GQWIgDHdevWTfv375ckhYeHa+/evQ5XBBMQYABcITIyUseOHZMkde3alfUTcV4EGADXuOKKK1g/EU1GgAFwle/XT+zQoYMGDx6sf//7306XBJciwAC4jsfjUVVVla65+mqNGjVK//jHP5wuCS5EgAFwJcuyVPLJJ8oeN04TJkzQUzNmOF0SXCbE6QIA4FwWv/aausfHa8ZTT2nXzp16OS/P6ZLgErwPDIAR5j3/vH45ZYpuvOEGrfT5nC4nYJk0dhJgAIzxxhtv6M4771Sc16udu3axfmIzMGnsJMAAGGX16tW64YYbJLF+YnMwaewkwAAYh/UTm49JYycBBsBI5eXl6tatmySpurpa4eHhDlcUGEwaO5lGD8BIcXFxqqqqkiR16NCB9RODEAEGwFgRERH11k/88ssvHa4ILYkAA2C009dPTE5O1tq1a/37amtrlZ+fr1OnTjlVHpoRAQbAeN+vnxgZEaFrr71Wb7zxhv7+0ktKjovTT++8U3kvv+x0iWgGTOIAEDCOHTumtm3bSpKubtNGzx0/rnaSRrRvr9KyMkVGRjpboAFMGjs5AwNgvEOHDil35kwlxMRoTGio3pT0yfHjGiIpVdKdJ07oN48+6nCVuNQIMADGKy8v19sFBWp94oQmHDumzDP2/+7ECS1fskTr1693pD40Dy4hAggItm2r4N//1q8mTVK3Awf0x6NH1f+0/XmSXuzbVx9t2iSPh7/dG2PS2MlPEUBAsCxLt4wapU3bt+vWWbN0U1iYHmjTRvv+d3+OpFY7d+oVPlssYHAGBiAgVVdX65knn1TeP/6hR2pq9Ghdnf4jaXhYmL7YsYMJHY0waezkDAxAQOrQoYP+MHeuPt60SZ8OG6beoaEqlXRnTQ0TOgIEZ2AAgsKaNWv06AMPqLqsTNuOH1fJunUaNGiQ02W5jkljJwEGIGicOnVKry5erP/30EPqEhentevXM6HjDCaNnQQYgKDz3Xff6bnnnlNCQoKys7OdLsdVTBo7CTAAQev48eNq06aN02W4ikljJwEGAPAzaezk4i8AwEgEGADASAQYAMBIrgmw119/Xf369VOrVq20YcOGRtsVFxcrOTlZSUlJmj17dgtWCABwE9cEWP/+/bVs2TL96Ec/arRNXV2dJk+erOLiYpWWlmrx4sX64osvWrBKAIBbhDhdwPeSk5PP26akpESJiYmKj4+XJGVnZys/P199+vRp5uoAAG7jmjOwpqioqFBcXJx/2+v1qqKiwsGKAABOadEzsMzMTO3bt++s78+aNUujRo067/0ty2qOsgAABmrRAHv77bd/0P1jY2NVXl7u3y4vL5fX6220/YwZM/y3MzIylJGR8YOeHwACjc/nk8/nc7qMi+K6lThuvPFGzZkzR1dfffVZ+2pra9W7d2+9++676tq1q9LS0rR48eIG/wdm0rvJAcAtTBo7XfM/sGXLlikuLk5r167VyJEjNWLECEnSnj17NHLkSElSSEiI5s2bp5tvvll9+/bVXXfdxQQOAAhSrjsDu1RM+isCANzCpLHTNWdgAABcCAIMAGAkAqwBps7IcQr9dWHorwtDf124YOkzAqwBwfLDv1TorwtDf10Y+uvCBUufEWAAACMRYAAAIwX0NHoAwIUzJRZcsxr9pWbKDwAAcHG4hAgAMBIBBgAwEgEm6fXXX1e/fv3UqlUrbdiwodF2xcXFSk5OVlJSkmbPnt2CFbpLVVWVMjMz1atXLw0bNkzV1dUNtouPj9eAAQOUmpqqtLS0Fq7SeU05XqZMmaKkpCSlpKRo48aNLVyhu5yvv3w+n8LDw5WamqrU1FTNnDnTgSrd4/7771d0dLT69+/faJuAP75s2F988YX95Zdf2hkZGfb69esbbFNbW2v37NnTLisrs2tqauyUlBS7tLS0hSt1h8cee8yePXu2bdu2nZubaz/++OMNtouPj7f379/fkqW5RlOOl4KCAnvEiBG2bdv22rVr7fT0dCdKdYWm9NeqVavsUaNGOVSh+6xevdresGGDfeWVVza4PxiOL87AJCUnJ6tXr17nbFNSUqLExETFx8erdevWys7OVn5+fgtV6C4rVqxQTk6OJCknJ0fLly9vtK0dpJNpmnK8nN6P6enpqq6uVmVlpRPlOq6pv1/Bejw1ZMiQIYqIiGh0fzAcXwRYE1VUVCguLs6/7fV6VVFR4WBFzqmsrFR0dLQkKTo6utFfCsuydNNNN2nQoEH6+9//3pIlOq4px0tDbXbv3t1iNbpJU/rLsix9+OGHSklJUVZWlkpLS1u6TKMEw/EVsNPoz5SZmal9+/ad9f1Zs2Zp1KhR571/sL2vrLH+euaZZ+ptW5bVaN988MEHiomJ0TfffKPMzEwlJydryJAhzVKv2zT1eDnzjCLYjrPvNeV1Dxw4UOXl5QoNDVVRUZHGjBmjLVu2tEB15gr04ytoAuztt9/+QfePjY1VeXm5f7u8vFxer/eHluVa5+qv6Oho7du3T126dNHevXvVuXPnBtvFxMRIkjp16qTbbrtNJSUlQRNgTTlezmyze/duxcbGtliNbtKU/goLC/PfHjFihCZNmqSqqipFRka2WJ0mCYbji0uIZ2jsGvugQYO0detW7dixQzU1NXrttdc0evToFq7OHUaPHq2FCxdKkhYuXKgxY8ac1ebYsWM6fPiwJOno0aN66623zjlbKtA05XgZPXq0Fi1aJElau3atOnTo4L80G2ya0l+VlZX+38+SkhLZtk14nUNQHF8OTiBxjX/961+21+u127RpY0dHR9vDhw+3bdu2Kyoq7KysLH+7wsJCu1evXnbPnj3tWbNmOVWu4/bv328PHTrUTkpKsjMzM+0DBw7Ytl2/v7766is7JSXFTklJsfv16xeU/dXQ8fLiiy/aL774or/NL37xC7tnz572gAEDGp0BGyzO11/z5s2z+/XrZ6ekpNjXXnut/dFHHzlZruOys7PtmJgYu3Xr1rbX67VffvnloDu+AnYtRABAYOMSIgDASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBIBBgAwEgEGADASAQYAMBI/wOTeS9vmAwv4QAAAABJRU5ErkJggg==\"\n",
       "  frames[18] = 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\"\n",
       "  frames[19] = \"data:image/png;base64,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\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animNVRRVDORWXFNVOVI = new Animation(frames, img_id, slider_id, 100, loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0xa809550>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from JSAnimation import IPython_display\n",
    "from matplotlib import animation\n",
    "\n",
    "# create a simple animation\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(xlim=(0, 10), ylim=(-2, 2))\n",
    "arrow = ax.arrow(0, 0, 1, 0, head_width=0.05, head_length=0.1, fc='k', ec='k')\n",
    "ax.set_xlim(-1.1, 1.1)\n",
    "ax.set_ylim(-1.1, 1.1)\n",
    "\n",
    "def init():\n",
    "    pass\n",
    "\n",
    "def animate(i):\n",
    "    ax.cla()\n",
    "    alpha = 6.28 * i / 20.\n",
    "    x = 1 * np.cos(alpha)\n",
    "    y = 1 * np.sin(alpha)\n",
    "    ax.arrow(0, 0, x, y, head_width=0.05, head_length=0.1, fc='r', ec='k')\n",
    "    ax.set_title(\"alpha = {:.2f} rad\".format(alpha))\n",
    "    \n",
    "animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                        frames=20, interval=100, blit=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyzing the differential rotation of a vector around a given angle "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section: analyze what happens around theta - alpha when theta becomes small."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Displaying the full kinematics of the Floyd Rose Vibrato "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here putting it all together around the small theta variation and showing a working model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}